1. Introduction
The design of aircraft is inherently a multi-disciplinary undertaking, during which data and information must be exchanged between multiple teams of engineers, each with expertise in a specific field. Managing the transmission, possibly translation and storage of data between collaborating groups is complex and error-prone. The adoption of a standardized, data-centric scheme for storage of all data improves consistency and reduces the risk of misconceptions and conflicts. In order to achieve this effectively, an initial effort must be made to develop suitable interfaces between the analysis modules and the data archive.
Furthermore, each phase of the design process poses different requirements on the fidelity and resolution of the design and analysis tools. For stability and control analysis, as well as for flight simulation, look-up tables for aerodynamic forces, moments and derivatives need to be generated. Different flight analysis tools require different tables/input formats. For example, the flight analyzer and simulator PHALANX [
1,
2,
3,
4] developed by Delft University of Technology requires a set of three-dimensional tables of force and moment coefficients with the effect of each control channel acting individually. Multi-fidelity aerodynamic modeling aims to cover the flight state parameter space of the entire flight envelope with an optimal distribution of computational resources. This again requires a standardized, data-centric scheme to host the data, which can be used for variable fidelities.
The label Li , where , is used to classify the fidelity level of a computational model and its software implementation:
- L0:
handbook methods, based on statistics and/or empirical design rules;
- L1:
based on simplified physics, can model and capture a limited amount of effects. For example, the linearized-equation models, the Vortex-Lattice Method (VLM) or the panel method in aerodynamics;
- L2:
based on accurate physics representations. For example, the non-linear analysis, Euler-based CFD;
- L3:
represents the highest end simulations, usually used to capture detailed local effects, but do not allow wide exploration of the design space due to computational cost. Additionally, the modeling may require extensive ad hoc manual intervention. For example, the highest fidelity methods, RANS-based CFD.
To construct a reasonable variable fidelity CFD analysis system, one should consider the variable fidelity of the geometrical representations corresponding to the CFD tools. The level of detail in the geometry gathered from a CAD system needs to match the CFD model fidelity. The chosen high fidelity model must be as accurate as possible and can reflect all considered complex flow characteristic; the chosen low-fidelity model must reflect the basic flow characteristics and be as effective as possible. In the conceptual design stage, the usual practice, for example, in the RDS [
5], the AAA [
6] and the VSP [
7] software systems, is to use a purpose-specific CAD that is simpler than the commercial systems, and fewer parameters need to be used for the configuration layout at this stage in the design cycle [
8]. However, for some innovative configurations, different ranges of flight conditions or more detailed analyses, the simplified CAD is not sufficient for a higher fidelity CFD analysis; thus, an enriched geometry definition with more parameters is needed. The Common Parametric Aircraft Configuration Schema (CPACS) [
9,
10], defining the aircraft configuration parametric information in a hierarchical way, gives the opportunity to incorporate different fidelity CFD tools with one single CPACS file. For different fidelity tools to be used, the corresponding geometry information can be imported/retrieved from the common CPACS file to match the model fidelity.
SUAVE, Standford University Aerospace Vehicle Environment [
11,
12,
13], which is also a multi-fidelity design framework developed at Stanford University, stores the aircraft geometry information using an inherent defined data class, which can be easily modified. The aerodynamic solutions can be generated from simple models within SUAVE or easily imported from external sources like CFD or wind tunnel results. The aircraft analysis in SUAVE is calculated with a so-called “fidelity zero” VLM to predict lift and drag, with a number of corrections such as the compressibility drag correction, parasite drag correction, etc. [
12], to adapt the VLM prediction to a wider range (transonic and supersonic flow regions). It incorporates the “multi-fidelity” aerodynamics through the provided response surface by combining the different fidelity data. However, currently, SUAVE is still working on connecting higher fidelity models directly to it; the response surfaces are only available to incorporate higher fidelity lift and drag data from the external sources [
12]. At this point, one cannot guarantee that the geometry information used for different fidelity tools is consistent during data exchanging, transferring and translating. Moreover, the prediction is only limited to lift and drag, so that it might not be easy for engineers to look into the physical details for a better design, for example, the pressure isobars and distributions, the laminar flows, transitions and the shock forming, etc. Thus, a dataset that can store complete and consistent information for different fidelity tools to solve the physical flows is desired. The CPACS-based multi-fidelity aerodynamic tools show a great consistency due to the one data-centric schema, and the automation of the progressive process can thus be implemented and realized with minimum data loss.
With all the computed aerodynamic data at hand, an important task is to construct surrogate models that integrate all analysis results computed by tools of different fidelity. Such data fusion applications are enabled by standardization of the data—format, syntax and semantics—of the aerodynamic simulation tools. The work in [
14] describes the workflow of an automatic data fusion process for CPACS [
9,
10]. The application was developed in the EU research project Aircraft 3rd Generation MDO for Innovative Collaboration of Heterogeneous Teams of Experts (AGILE) [
15], where every module (the aerodynamic module, the sampling module, the surrogate modeling module) communicates by CPACS files.
This paper will address other aspects of the work in [
14], namely how the different fidelity tools in the aerodynamic module communicate and how a look-up table of the aero-dataset can be obtained automatically from the tools (L1 and L2 in this paper).
Section 2 describes the CPACS file definition in more detail, especially the geometry definitions, which are important for CFD mesh generators.
Section 3 details the CPACS interfaces for variable fidelity analysis.
Section 4 gives an overview of the CFD flow solvers used in the work.
Section 5 presents the applications to the test case using variable fidelity tools.
Section 6 discusses different modeling approaches for control surfaces used for Euler simulations, and finally,
Section 7 summarizes the conclusions of the work.
1.1. Background
AGILE is an EU-funded Horizon 2020 project coordinated by the Institute of Air Transportation Systems of the German Aerospace Center (DLR). Its objective is to implement a third generation multidisciplinary optimization process through efficient collaboration by international multi-site design teams. The 19 partners bring different knowledge and competences regarding aircraft design and optimization. As mentioned above, such a collaboration is enabled by the adoption of a common data storage format. To this end, AGILE relies on the XML format CPACS (Common Parametric Aircraft Configuration Schema) [
9,
10] in development at DLR since 2005.
The RCE (Remote Component Environment) integration environment and workflow manager [
16] controls and executes the sequence of analysis modules and manages the data transport and translation, as well as logging the process. RCE makes it easy to set up an MDO workflow also with modules running on remote hosts. That is handled by the BRICS (Building blocks for mastering network Restrictions involved in Inter-organisational Collaborative engineering Solutions) [
17] system, which supports remote execution and data transport. The request can be with “engineer in the loop” for a remote expert to run the calculation or for an automated workflow to be run without user intervention. The input is generally a CPACS file containing all the information required. The new data generated are added to the CPACS file and sent back to the requester. More details about the AGILE collaborative approach can be found in [
18,
19].
The variable fidelity aerodynamic tools read a CPACS file, analyze the corresponding information extracted from the file, run the calculation and store the new data (e.g., aero-data tables) back to the CPACS file. CPACS supports a very flexible user-defined node feature (
cpacs.toolspecific) to handle parameters for the computational models, which are relevant only for a specific tool [
20].
1.2. Aerodynamic Model Description
The test case is the reference aircraft used in AGILE, a regional jet-liner, which was analyzed and simulated using the AGILE MDO system, without experimental data. This virtual aircraft is similar to an Airbus 320 or a Boeing 737. The reference aircraft is defined in CPACS [
9] format, shown in
Figure 1. Its aspect ratio is 9.5, and the detailed information of the airfoils along the aircraft span is shown in
Figure 2.
Figure 2a shows the plots of the airfoil along the three stations of the semi-span (
), with the root at 0%, the kink at 40% and the tip at 100%.
Figure 2b shows the maximum thickness and cambers per chord along the semi-span, as well as the corresponding locations of the local chords. It should be noted that the design exercises are carried out as if in an early design stage, so for instance, no engine is modeled. The configuration was also used in previous studies, to benchmark the conceptual design software CEASIOM [
20] and to validate the AGILE data fusion tool [
14] for building multi-fidelity aero-datasets. Some of the results shown in this paper are consistent with the previous simulations in [
14,
20], that the configuration is unchanged and the same CPACS file for geometry definition is used to assure a consistent and continuous investigation of the tools and methods.
4. Flow Solvers
The CFD (fidelity level L2–3) codes SU2 [
29,
31] and Edge [
28] are used for Euler and RANS flow modeling.
Edge is the Swedish national CFD code for external steady and unsteady compressible flows. Developed by the Swedish Defense Research Agency (FOI), it uses unstructured grids with arbitrary elements and an edge-based formulation with a node-centered finite-volume technique to solve the governing equations. Edge supports a number of turbulence models, as well as LES and DES simulations.
The SU2 [
29] software suite from Stanford University is an open-source, integrated analysis and design tool for complex, multi-disciplinary problems on unstructured computational grids. The built-in optimizer is a Sequential Least Squares Programming (SLSQP) algorithm [
32] from the SciPy Python scientific library. The gradient is calculated by continuous adjoint equations of the flow equations [
29,
31]. SU2 is in continued development. Most examples pertain to inviscid flow, but also, RANS flow models with the Spalart–Allmaras and the Menter’s Shear Stress Transport (SST)
turbulence models can be treated.
Figure 12 shows the comparison of the aerodynamic coefficients computed by Euler equations in SU2 and Edge for two different meshes of the reference aircraft. “Mesh-4p” has 4.0 million cells, and “mesh-2p” has 1.9 million cells. The meshes have the same meshing parameter settings as described in [
20]. Both have refined wing leading and trailing edges, and “mesh-4p” has settings for even smaller minimum dimensions of the cells. According to the mesh study in [
20], the predictions from both solvers converge as the mesh resolution increases, and “mesh-4p” was selected in [
20] for all the simulations carried out by SU2 by considering both computational accuracy and efficiency. In this paper, more simulations are made for both “mesh-2p” and “mesh-4p” using both Edge and SU2 for different flight conditions. For “mesh-2p”, Edge and SU2 give fairly close predictions for the aerodynamic coefficients
,
and
at Mach = 0.78 and 0.9. In the current study, we will use “mesh-4p” for the Euler solutions by SU2 in
Section 5 and “mesh-2p” for the calculations on control surface modeling in
Section 6, where SU2 and Edge are used to compare the geometry modeling approaches.